To most of us, these equations might as well be hieroglyphics. Scientists speak a different language to present issues, argue points and convey information. B efore many of these equations make it into a research journal or textbook, they are written in marker, chalk or ink. They are scratched out, erased and rewritten until they speak a universal truth backed by laws of mathematics or physics.

To most of us, these equations might as well be hieroglyphics.

Scientists speak a different language to present issues, argue points and convey information. B efore many of these equations make it into a research journal or textbook, they are written in marker, chalk or ink. They are scratched out, erased and rewritten until they speak a universal truth backed by laws of mathematics or physics.

We wanted to know what it is like to speak this language, to get lost in an equation. So we asked scientists from three Ohio universities to translate.

Daniel Phillips

physics professor, Ohio University

I like to calculate. Always have. Batting averages. Distances between cities. Interest earned. Itís one reason I became a physicist. Like most 5-year-olds, I like to ask ďWhy?Ē Physicists ask the same question but then try to answer the question with numbers.

That process involves a lot of equations. Itís not that we love equations for their own sake, although Iím sure some of my students think I do. Itís that equations provide a rigorous way for us to tease out the consequences of our understanding of nature. We can start with a statement such as ďlight is a waveĒ and figure out what numbers youíll see in a lab experiment if thatís true or if (light) is something else, such as a particle.I sit down with pen and paper and start out with a statement. Then I encode it as an equation and use algebra to work out how to rewrite that equation as something else. Then I use more algebra to rewrite the next equation as something else, and so on and so on, until eventually I have a prediction for an experiment.Itís really remarkable that mathematics will let you make predictions about the world around us.But one really needs to concentrate. If you get the math wrong, youíll make the wrong prediction. And the calculations go on for several (10, 20, sometimes more) pages.Sometimes though, you just know youíve got it right because everything falls into place at the end of the calculation. Things cancel out just the way they should, or two different ways of calculating the same quantity give the same answer. In some cases, the result is too beautiful not to be true.That makes all the pages of algebra worthwhile.

Jay Newby

post-doctoral mathematics researcher, Ohio State University

I use a whiteboard to interact with someone ó either students or colleagues.In this case, (fellow post-doc researcher) Mike Schwemmer and I were solving a problem, and the whiteboard is a many-layered record of the ideas that we were throwing back and forth.It is a difficult process because we have to think about the physical problem we want to solve and how the math works. But the two always go together ó figuring out the math helps us to better understand the physics, and that can be very exciting.That is why this whiteboard has a lot of doodles and drawings alongside the equations. There are so many different colors because when one of us had an idea, we would just pick up the closest marker and start talking.Sometimes the marker goes dry and you pick up a new one, and it might not even be the same color.After a few days of this, the whiteboard starts to look a little crazy.

Steven Izen

professor of mathematics, Case Western Reserve University

Written mathematics can be used to communicate or to help formulate and clarify ideas too complex to work out in oneís head.We submit our papers electronically, and our presentations at conferences and seminars are largely computer-prepared. But for work done on the fly, we write on surfaces ó paper, whiteboards or blackboards.Whiteboards and blackboards are ideal for interactive communication. Recently, I have been to several talks during which the speaker had his or her presentation displayed on a computer projector. But when questions were asked, the presenter used a whiteboard to quickly express the mathematical idea.Whiteboards and blackboards can be used to tell a story. Concepts can be developed in a sequential way, at a pace which the storyteller controls. The audience canít jump ahead, and in a properly designed classroom, the important parts of the story can be highlighted and remain visible as the story progresses. Details can be easily inserted.Personally, I prefer a whiteboard. When I teach in a classroom with a blackboard, I return to my office covered with chalk dust. A common quip is that I suffer from white lung disease.

David Drabold

physics professor, Ohio University

Much of my work involves the solution of the Kohn-Sham equations, which accurately describe the chemistry, chemical bonding, energetics and atomic structure of many advanced materials.When coupled with Newtonís second law, these equations provide predictions for the dynamical behavior of materials and molecules.The solutions are emergent ó the solutions represent properties characteristic of large collections of atoms, impossible to infer from the equations for a few particles.Many of the important processes of nature are encoded in a deeply inscrutable way in these equations. Conventional mathematical pondering is necessary but not sufficient here.These equations cannot be solved in interesting cases by mortal hand; for this we need the help of powerful computers. So the venerable act of pondering is transformed instead into an exploration with a computer and sophisticated codes that reveal the equations to the machine.For our part, we specify the problem and the background conditions we want to explore. Many discoveries are waiting to be uncovered with this modern variant of pondering.

Harsh Mathur

physics professor, Case Western Reserve University

I seldom work alone at a blackboard. For solitary work, I prefer pen on paper accompanied by espresso or black tea. White paper for preliminary scratch work, yellow paper for recording the solutions that emerge.But on rare occasions, I use a blackboard for solitary work. It sometimes just helps to see a problem written large on a blackboard. It helps overcome the physics equivalent of writerís block.And sometimes it is good to transcribe a hard-won solution from yellow paper to blackboard, to understand the full ramifications ó and to simply gloat.Blackboards are indispensable for collaboration and communication. One person writes on the board at a time; the others record the progress on notepads. Like mountaineers roped together, we are committed to exploring a single route at a time from among the myriad alternatives that compete for our attention. A typical project begins with simple questions. Once these questions have been given a precise mathematical formulation, the fun begins.The big moment, of course, is when all the pieces of the puzzle come together. Hundreds of pages of calculation will go into the production of a paper that might occupy just four pages in Physical Review Letters. There is no better medium for communication.One professor I knew in graduate school had become so reliant on blackboards that even during casual conversations outdoors he would write in the air as he spoke. To make matters worse, he would refer to his air inscriptions, pointing to them as though they were visible for all to see.

John Beacom

Astronomy, physics professor, Ohio State University

How do you figure out something when you canít see it? Or maybe it doesnít even exist yet?How do you communicate your understanding to others? Architects draw pictures of possible buildings. Football coaches sketch diagrams of possible plays. Scientists do something similar using pictures, equations and words.Much of what we work on in physics and astronomy is beyond the reach of our senses and requires special instruments to observe. We canít touch an atomic nucleus or visit a distant galaxy. And understanding these things requires abstract and complicated ideas, such as quantum mechanics and relativity.It gets worse ó doing research means working on things we donít understand yet.To figure out new things, we talk about them. Invariably, someone starts sketching things on a whiteboard or blackboard, a notepad or even a spare napkin. If we were trying to figure out a Rubikís Cube, we would be passing it around and fiddling with it, everyone trying different things.Millions of years of evolution have made our brains very efficient at using information from our senses. To activate those abilities, we need something we can see and touch, so we sketch and write, with everyone looking on and commenting.msomerson@dispatch.com@MarkSomerson